CN103294893A - Machine learning method for reducing inconsistency between traditional Chinese medicine subjective questionnaires - Google Patents

Abstract

The invention discloses a machine learning method for reducing the inconsistency between traditional Chinese medicine subjective questionnaires. The machine learning method comprises the following steps that 1), subjective questionnaire data is vectorized, wherein a subjective questionnaire consists of questions, weight and point values, and the vectorization allows a structure of the questionnaire to be converted into a vector; 2), a consistency target of questionnaire groups is defined and expressed; a contradiction function C(x) is defined to express the consistency between the questionnaire groups; the contradiction function takes a value obtained by converting a point value of the questionnaire group as an input, wherein negative correlation serves as the contradiction function in the process, and accords with a statistical learning theory; 3), main subjective questionnaires such as an NPQ (Nonverbal Personality Questionnaire), an MPQ (Mcgill Pain Questionnaire) and an SF-36 (Short Form-36) used by traditional Chinese medicine are subjected to consistency analysis, wherein each of the NPQ and the MPQ has a sub-questionnaire, and the SF-36 has eight sub-questionnaires; the following objective function of the consistency is defined according to the contradiction function in Step 2); and 4), the objective function is solved. The machine learning method reduces the inconsistency between results of different traditional Chinese medicine treatment effect evaluation questionnaires, and improves the accuracy of the evaluation on a traditional Chinese medicine treatment effect.

Description

A kind of machine learning method that reduces subjective the differing property of questionnaire of the traditional Chinese medical science

Technical field

The present invention is a kind of machine learning method that reduces subjective the differing property of questionnaire of the traditional Chinese medical science, belongs to the renovation technique of the machine learning method that reduces subjective the differing property of questionnaire of the traditional Chinese medical science.

Background technology

Survey is a kind of data collect means that social investigation causes.To be investigator's questionnaire of using unified design go and find out what's going on or the investigation method of consultation to the respondent who is selected for it.Survey is to write in a kind of research method that the mode of problem is gathered information.Survey is a kind of research mode of excavating true present situation, maximum purpose is to collect, accumulate the basic document of every education of science attribute of a certain target group, should consider and whether can reach goal in research smoothly and note the fitness of research sample on questionnaire.But there is subjectivity in survey.

In the Chinese traditional treatment process, the doctor needs to be grasped patient's subjective sensation with the order of severity of judgement disease and the effect for the treatment of.The result of cervical spondylopathy patient treatment report is the theory and technology based on psychometrics, obtains the patient in daily life, healthy impression with to the physical experience of aspects such as treatment measure subjectivity satisfaction by forms such as interview, self-appraisal questionnaires.Pain is a kind of subjective symptom of patient's perception, still is difficult to the service-strong objective indicator at present and measures.More accurate in order to make the subjective sensation measurement, researchers have designed the various questionnaires (scale) at different aspect.As in the treatment of cervical spondylopathy, use three kinds of different questionnaires of NPQ, MPQ and SF-36 to determine the sensation of patient's cervical spondylopathy usually, wherein NPQ and MPQ are for the questionnaire of weighing pain degree, and SF-36 is used for weighing life quality.In the treatment of the knee joint of orthopaedics, adopt WOMAC and SF-36 to determine the kneed sensation of patient usually, wherein WOMAC is the scale of international knee osteoarthritis, SF-36 is with aforementioned consistent.Patient after having answered each questionnaire, score values that can have one or more processes to add up and obtain all, wherein NPQ, MPQ and WOMAC are a score value, and SF-36 has 8 score values, represents the different aspect of life quality respectively.

The doctor rule of thumb judges patient's state then mainly by observing the data of several questionnaires simultaneously at present, or judges the effect for the treatment of according to the lifting of the score value of twice questionnaire before and after the treatment.Through regular meeting's inconsistent situation of patient condition that questionnaire shows of coming out, as a certain patient NPQ questionnaire is shown that its pain index is very high, but the SF-36 questionnaire shows that again its life quality is pretty good but in practice; Twice MPQ value is to have risen before and after a certain patient, and the pain increased to show it, but the NPQ score value descended, and shows that its pain slows down.When the doctor faces this situation, can only carry out subjective judgement according to the experience of self, be used for addressing this problem and also have special technology at present.

Above questionnaire all is that its theoretical foundation and correctness are undoubted through the medical science of strictness demonstration, and the generation of this contradiction mainly is the subjective deviation when being answered by patient, and dissimilar questionnaires has different potential weights to cause to different patients.

Summary of the invention

The objective of the invention is to consider the problems referred to above and inconsistency between a kind of result who lowers different Chinese traditional treatment recruitment evaluation questionnaires is provided, to improve the machine learning method of subjective the differing property of questionnaire of the minimizing traditional Chinese medical science of accuracy that its centering is cured the assessment of therapeutic effect.The present invention is convenient and practical.

Technical scheme of the present invention is: the machine learning method of subjective the differing property of questionnaire of the minimizing traditional Chinese medical science of the present invention comprises the steps:

1) the subjective questionnaire data of vectorization: subjective questionnaire is made of problem, weight and score value, and vectorization is the thaumatropy of questionnaire vector, establishes subjective questionnaire and is expressed as Q={q ₁, q ₂..., q _m, q wherein _iIt is the score of i questionnaire item;

2) the consistance target of definition questionnaire group, and formalization is expressed; Definition contradiction function C (x) is expressed consistance between the questionnaire group, the contradiction function with the score value of questionnaire group through the value that obtains after the conversion as input, this process uses negative correlation as the contradiction function, coincidence statistics is practised theoretical;

3) main subjective questionnaire NPQ, MPQ and the SF-36 that the traditional Chinese medical science is used carries out consistency analysis, and wherein NPQ and MPQ respectively have a sub-questionnaire, and SF-36 has 8 sub-questionnaires, according to the 2nd) the contradiction function in step, define following conforming target:

$\underset{\mathrm{\Φ}}{\max }\mathrm{corr}\left({\mathrm{\φ}}_1\left(\mathrm{NPQ}\right)\right),{\mathrm{\φ}}_2(\mathrm{MPQ}\left)\right),{\mathrm{\φ}}_3(\mathrm{SF}-{36}_1),\·\·\·,{\mathrm{\φ}}_{10}(\mathrm{SF}-{36}_8))$

（1）

In (1) formula, corr represents the computing function of correlativity;

4) to the finding the solution of (1) formula, think that Φ has following linear forms: Φ (x)=w ^TX, owing to used the nuclear mapping, so its result can not be subjected to the restriction of the linear combination of basis function, used the thought that is similar to KCCA that the optimization problem shown in (1) formula is found the solution, release the maximized solution of consistance between two groups of questionnaires earlier, and then be generalized to the situation of many group questionnaires; Be example with NPQ and two groups of questionnaires of MPQ, establish it and have scale l, i.e. NPQ={NPQ ₁, NPQ ₂..., NPQ _lAnd MPQ={MPQ ₁, MPQ ₂..., MPQ _l, establish u=M _N* NPQ, υ=M _M* MPQ; Make the correlativity maximum of u and υ, be equivalent to and find the solution following optimization problem:

$\underset{M_N,M_M}{\max }\frac{E\left[\mathrm{u\υ}\right]}{\sqrt{E\left[u^2\right]E\left[{\mathrm{\υ}}^2\right]}}---\left(3\right)$

E[wherein] be mathematical expectation, note C _{NPQ, MPQ}Be covariance matrix, then (2) can be expressed as:

$\underset{M_N,M_M}{\max }\frac{M_N^T{C}_{N,M}{M}_M}{\sqrt{M_N^T{C}_{N,N}{M}_N{M}_M^T{C}_{M,M}{M}_M}}---\left(4\right)$

According to the KCCA theory, in optimization aim (3), consider u ^TU and υ ^Tυ rather than original u and υ help to introduce kernel function in optimization aim; Quote two standardization items:

With

It only calculates for simplifying, and can't influence the optimization aim of (3); Simultaneously, as long as levying the dimension in space, the data point number bit of training wants big, the optimum solution of (3)

With

One fixes on set span{ φ (x ₁), φ (x ₂) ..., φ (x _n) and

In, wherein x and y are respectively the training sample points of NPQ and MPQ, namely $M_M^{*}={\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\mathrm{\φ}\left(x_i\right),$

Use the mode of maximum likelihood to control the model complexity, increase by two regularization term about α and β, obtain following optimization aim expression formula:

$\underset{\mathrm{\α},\mathrm{\β}}{\max }{\mathrm{\α}}^T{K}_X{K}_Y\mathrm{\β}-{\mathrm{\η}}_{\mathrm{\α}}{\left|\right|\mathrm{\α}\left|\right|}^2-{\mathrm{\η}}_{\mathrm{\β}}{\left|\right|\mathrm{\β}\left|\right|}^2---\left(4\right)$

K wherein _X=Σ _iφ (x _i) ^Tφ (x _i),

(4) formula is and finds the solution target.

The represented optimization aim of above-mentioned formula (4) adopts the enclosed solving method to find the solution:

Note w=(α ^T, β ^T) ^T, then being had by representation theorem, the optimum solution of (4) is equivalent to secular equation B ^-1The solution of Aw=pw, p can regard square formation B as ^-1The proper vector of A, wherein:

$A=\left(\begin{array}{cc}0& K_X{K}_Y\\ K_Y{K}_X& 0\end{array}\right)$ $B=\left(\begin{array}{cc}{K}_X{K}_Y& 0\\ 0& K_Y{K}_X\end{array}\right)---\left(5\right)$

Step to above-mentioned solving-optimizing target is carried out following conclusion:

The 1st step: input questionnaire group Q _iAnd Q _j

The 2nd step: calculate questionnaire group Q _iAnd Q _jThe Gram matrix based on radial basis function nuclear

With

The 3rd step: use formula (5) to calculate questionnaire group Q _iAnd Q _jCorrespondence With

The 4th step: compute matrix

With

Proper vector

With

The 5th step: output is as transformation matrix;

Top step is the enclosed solving method, can directly from training data, obtain transformation matrix, but because it will carry out the feature decomposition of matrix, therefore be only applicable to the little situation of amount of training data, be not more than 1000 examples, use a kind of based on the method for decomposing the index iteration convergence, respectively questionnaire group consistance is separately found the solution, connecting mapping then merges, algorithm uses a w at random as initial value, correlativity is once calculated in every optimization one time, and twice correlativity change is less than 0.5% the time when front and back, and algorithm finishes.

The represented optimization aim of above-mentioned formula (4) adopts following steps to find the solution:

The 1st step: input questionnaire group Q _iAnd Q _j, initializes weights vector w;

The 2nd step: calculate questionnaire group Q _iAnd Q _jThe Gram matrix based on radial basis function nuclear

With

The 3rd step: the Gram matrix K based on radial basis function nuclear of calculating weight vectors w _w

The 4th step: use formula (5), calculate questionnaire group Q _iAnd Q _j

With

The 5th step: compute matrix

With

Proper vector With

The 6th step: upgrade $w=M_{Q_i}{M}_{Q_j};$

The 7th step: calculate δ=corr (Q _i* w, Q _j* w);

The 8th step: if δ＞0.5% then jumped to for the 3rd step, otherwise finishes;

Said process is the complexity that exchanges algorithm with the time for, has avoided big square formation is directly carried out feature decomposition, comes down to each composition is carried out based on the finding the solution of method one, and then carries out addition;

Because what said process carried out is to connect after optimizing again, therefore need one to connect the step result is connected, adopt the method shown in the following formula (6) to connect, its objective is the expression formula that obtains an expansion mapping, can be used for the data in future;

$\mathrm{\φ}\left(x\right)=({\mathrm{\Σ}}_i{Q}_i/|\left|M_{Q_i}\right||+{\mathrm{\Σ}}_i{Q}_j/|\left|M_{Q_j}\right|\left|\right)x---\left(6\right)$

By formula (6), obtain a conversion that can be used for any unknown data It can change the distribution of unknown data, makes it and existing questionnaire group Q _iAnd Q _jScore value correlativity maximum.

The present invention is owing to adopt by conversion of historical questionnaire data study, and under the effect of this conversion, the inconsistency between the questionnaire reduces to minimum, eliminates the subjective deviation of patient when answering a questionnaire to greatest extent, makes it more to be conducive to doctor's diagnosis.Invention is the machine learning method of subjective the differing property of questionnaire of a kind of convenient and practical minimizing traditional Chinese medical science.

Embodiment

Embodiment:

In the present embodiment, the present invention reduces the inconsistency between the questionnaire to greatest extent by a conversion that acts on existing questionnaire data.For effective solution of clear expression, at first problem is carried out formal description.Be provided with the questionnaire data set

Q={Q ₁, Q ₂..., Q _m, Q wherein _iBe the vector of n * 1, represent the score value of i questionnaire, then target of the present invention is to seek a conversion Φ by machine learning method, makes contradiction functional value C (Φ (the Q)) minimum of definition on it.In the present invention, the consistency problem of a questionnaire fractional value that consideration changes namely reduces the inconsistency that changes between the twice questionnaire mark in treatment front and back, even C is (Φ (Q ^T+1)-Φ (Q ^t)) minimum, consider the convenience in the calculating, target is decided to be the correlativity maximum that makes through between the questionnaire mark after the Φ conversion.

The present invention adopts a kind of Kernel of being similar to Canonical Correlation Analysis(KCCA) method obtain optimum Φ value.The particular content of invention is described below:

With NPQ, the consistance of MPQ and three groups of questionnaires of SF-36 is that example describes.Because SF-36 has 8 score values, and NPQ and MPQ have only a score value, so establish Φ={ φ ₁..., φ ₁₀, target is:

$\underset{\mathrm{\Φ}}{\max }\mathrm{corr}\left({\mathrm{\φ}}_1\left(\mathrm{NPQ}\right)\right),{\mathrm{\φ}}_2(\mathrm{MPQ}\left)\right),{\mathrm{\φ}}_3(\mathrm{SF}-{36}_1),\·\·\·,{\mathrm{\φ}}_{10}(\mathrm{SF}-{36}_8))---\left(5\right)$

Set Φ and have following linear forms: Φ (x)=w ^TX, owing to used the nuclear mapping among the present invention, so its result can not be subjected to the restriction of the linear combination of basis function.Use is similar to the thought of KCCA the optimization problem shown in (1) formula is found the solution, and releases the maximized solution of consistance between two groups of questionnaires earlier, and then is generalized to the situation of many group questionnaires.Be example with NPQ and two groups of questionnaires of MPQ, establish it and have scale l, i.e. NPQ={NPQ ₁, NPQ ₂..., NPQ _lAnd MPQ={MPQ ₁, MPQ ₂..., MPQ _l, establish u=M _N* NPQ, υ=M _M* MPQ.Make the correlativity maximum of u and υ, be equivalent to and find the solution following optimization problem:

$\underset{M_N,M_M}{\max }\frac{E\left[\mathrm{u\υ}\right]}{\sqrt{E\left[u^2\right]E\left[{\mathrm{\υ}}^2\right]}}---\left(6\right)$

E[wherein] be mathematical expectation, note C _{NPQ, MPQ}Be covariance matrix, then (2) can be expressed as:

$\underset{M_N,M_M}{\max }\frac{M_N^T{C}_{N,M}{M}_M}{\sqrt{M_N^T{C}_{N,N}{M}_N{M}_M^T{C}_{M,M}{M}_M}}---\left(7\right)$

According to the KCCA theory, in optimization aim (3), consider u ^TU and υ ^Tυ rather than original u and υ help to introduce kernel function in optimization aim.Quote two standardization items:

With

It only calculates for simplifying, and can't influence the optimization aim of (3).Simultaneously, as long as levying the dimension in space, the data point number bit of training wants big, the optimum solution of (3) With

One fixes on set span{ φ (x ₁), φ (x ₂) ..., φ (x _n) and

In, wherein x and y are respectively the training sample points of NPQ and MPQ, namely $M_M^{*}={\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\mathrm{\φ}\left(x_i\right),$

Use the mode of maximum likelihood to control the model complexity, increase by two regularization term about α and β, obtain following optimization aim expression formula:

$\underset{\mathrm{\α},\mathrm{\β}}{\max }{\mathrm{\α}}^T{K}_X{K}_Y\mathrm{\β}-{\mathrm{\η}}_{\mathrm{\α}}{\left|\right|\mathrm{\α}\left|\right|}^2-{\mathrm{\η}}_{\mathrm{\β}}{\left|\right|\mathrm{\β}\left|\right|}^2---\left(4\right)$

K wherein _X=Σ _iφ (x _i) ^Tφ (x _i),

(4) formula is the target of finding the solution of the present invention.

The present invention proposes to adopt two kinds of methods that (4) represented optimization aim is found the solution.Method one is the enclosed solving method.Note w=(α ^T, β ^T) ^T, then being had by representation theorem, the optimum solution of (4) is equivalent to secular equation B ^-1The solution of Aw=pw, p can regard square formation B as ^-1The proper vector of A, wherein:

$A=\left(\begin{array}{cc}0& K_X{K}_Y\\ K_Y{K}_X& 0\end{array}\right)$ $B=\left(\begin{array}{cc}{K}_X{K}_Y& 0\\ 0& K_Y{K}_X\end{array}\right)---\left(5\right)$

1 pair of above-mentioned steps of algorithm is concluded.

The 1st step: input questionnaire group Q _iAnd Q _j

The 2nd step: calculate questionnaire group Q _iAnd Q _jThe Gram matrix based on radial basis function nuclear With

The 3rd step: use formula (5) to calculate questionnaire group Q _iAnd Q _jCorrespondence

With

The 4th step: compute matrix With

Proper vector

With

The 5th step: output is as transformation matrix

Top step is the enclosed solving method, can directly obtain transformation matrix from training data, but because it will carry out the feature decomposition of matrix, therefore is only applicable to the little situation of amount of training data (being not more than 1000 examples).Therefore we use a kind of based on the method for decomposing the index iteration convergence in the present invention, respectively questionnaire group consistance is separately found the solution, connecting mapping then merges, algorithm uses a w at random as initial value, correlativity is once calculated in every optimization one time, twice correlativity change is less than 0.5% the time when front and back, and algorithm finishes.Method two is the complexity that exchanges algorithm with the time for, has avoided big square formation is directly carried out feature decomposition, comes down to each composition is carried out based on the finding the solution of method one, and then carries out addition.The key step of method two method for solving is summarized as follows:

The 1st step: input questionnaire group Q _iAnd Q _j, initializes weights vector w

The 2nd step: calculate questionnaire group Q _iAnd Q _jThe Gram matrix based on radial basis function nuclear

With

The 3rd step: the Gram matrix K based on radial basis function nuclear of calculating weight vectors w _w

The 4th step: use formula (5), calculate questionnaire group Q _iAnd Q _j

With

The 5th step: compute matrix

With Proper vector

With

The 6th step: upgrade $w=M_{Q_i}{M}_{Q_j}$

The 7th step: calculate δ=corr (Q _i* w, Q _j* w)

The 8th step: if δ＞0.5% then jumped to for the 3rd step, otherwise finishes

Because what method two carried out is to connect after optimizing again, therefore need a connection step that the result is connected, we adopt the method shown in the formula (6) to connect in the present invention, its objective is the expression formula that obtains an expansion mapping, can be used for following data.

$\mathrm{\φ}\left(x\right)=({\mathrm{\Σ}}_i{Q}_i/|\left|M_{Q_i}\right||+{\mathrm{\Σ}}_i{Q}_j/|\left|M_{Q_j}\right|\left|\right)x---\left(6\right)$

By formula (6), obtain a conversion that can be used for any unknown data It can change the distribution of unknown data, makes it and existing questionnaire group Q _iAnd Q _jScore value correlativity maximum.

Content of the present invention is concentrated at the cervical spondylopathy of certain institute of traditional Chinese medicine and orthopaedics clinical data and has been carried out application testing, has all obtained effect preferably.

The result of cervical spondylopathy patient treatment report is the theory and technology based on psychometrics, obtains the patient in daily life, healthy impression with to the physical experience of aspects such as treatment measure subjectivity satisfaction by forms such as interview, self-appraisal questionnaires.Pain is a kind of subjective symptom of patient's perception, still is difficult to the service-strong objective indicator at present and measures.At the deficiency of domestic similar research on the scientific research and design methodology, introduce NPQ cervicodynia scale, McGill pain scale (MPQ) and the SF-36 life quality scale patient subjective assessment index of international endorsement as therapeutic evaluation, carried out comprehensive evaluation from aspects such as pain relief, functional rehabilitation, life qualities.

Adopted the patient data of 794 examples from different branches in this test, each patient record the subjective questionnaire score value in 5 stages to represent the order of severity of its cervical spondylopathy, be respectively before the treatment, treatment beginning 1 month, treatment finish, treatment finished back 1 month and treatment finishes back 3 months.Ideal situation is that the variation of all indexs is all synchronous, and following three kinds of possibilities occur but actual conditions are meetings: synchronously, part is synchronous and asynchronous.Synchronously: in therapeutic process, the variation of NPQ, MPQ and SF-36 is consistent, and as the treatment through a period, NPQ and MPQ descend, and SF-36 rises, and shows treatment pain decline afterwards, and life quality rises, and such three indexs are synchronous; Part is synchronously: in therapeutic process, the variation of NPQ, MPQ and SF-36 is not quite identical, in certain treatment stage, the phenomenon that NPQ descends, MPQ rises occurs, and then the doctor can't judge that the patient alleviates through the pain after the treatment or increased the weight of; Asynchronous: the phenomenon of subjective questionnaire contradiction has all appearred in each treatment stage in therapeutic process.

Be synchronously with explanatory note explanation, part synchronously and asynchronous, not with scheming (seeing above-mentioned blue literal)

For nonsynchronous index, the doctor has been difficult to judge the effect for the treatment of.Therefore adopted method of the present invention to improve consistance between the different indexs in clinical, table 1 has showed that the consistance that Guangdong Provincial TCM Hospital cervical spondylopathy index gathers improves degree:

Table 1. gathers the raising degree of indicator consilience

The present invention also uses at the treatment of cervical spondylopathy achievement data of each branch and concentrates, and table 2 has showed that the indicator consilience of different branches after using the present invention improves degree:

Table 2. gathers the raising degree (NPQ vs MPQ) of indicator consilience

Annotate: employed data from " national Eleventh Five-Year Plan science and technology support planning item: the clinical research of different acupuncture-moxibustion therapy method treatment cervical spondylopathy cervicodynia prioritization schemes, bullets: 2006BAI12B04-1 "

The present invention can significantly improve the consistance between the index as can be seen, is conducive to the doctor and diagnoses.

6.2 the clinical trial of orthopaedics data

Adopt at random, contrast, polycentric test design, for the knee osteoarthritis patient who meets the standard of including in, accept traditional Chinese medicine for oral administration, external application Chinese medicine, gimmick, acupuncture, the treatment of traditional medicine synthetic therapy scheme respectively, and carry out simultaneously in 5 tame hospitals.Adopt international osteoarthritis research scale (WOMAC), life quality scale (SF-36) to carry out observation of curative effect, form the suitable prioritization scheme of promoting with the effect characteristics of clear and definite above therapy and after analysis-by-synthesis.

Since WOMAC scale and SF-36 scale, and inconsistency can appear between 8 territories of SF-36 scale itself, and use the present invention reduces the inconsistent degree between these indexs.Table 3 has been showed in Guangdong Provincial TCM Hospital " research of the knee osteoarthritis Chinese medicine scheme optimization " project raising situation of using consistent degree after the method for the present invention.

The correlativity of table 3. orthopaedics index WOMAC and life quality index S F-36

Claims (3)

1. a machine learning method that reduces subjective the differing property of questionnaire of the traditional Chinese medical science is characterized in that comprising the steps:

1) the subjective questionnaire data of vectorization: subjective questionnaire is made of problem, weight and score value, and vectorization is the thaumatropy of questionnaire vector, establishes subjective questionnaire and is expressed as Q={q ₁, q ₂..., q _m, q wherein _iIt is the score of i questionnaire item;

2) the consistance target of definition questionnaire group, and formalization is expressed; Definition contradiction function C (x) is expressed consistance between the questionnaire group, the contradiction function with the score value of questionnaire group through the value that obtains after the conversion as input, this process uses negative correlation as the contradiction function, coincidence statistics is practised theoretical;

3) main subjective questionnaire NPQ, MPQ and the SF-36 that the traditional Chinese medical science is used carries out consistency analysis, and wherein NPQ and MPQ respectively have a sub-questionnaire, and SF-36 has 8 sub-questionnaires, according to the 2nd) the contradiction function in step, define following conforming target:

$\underset{\mathrm{\Φ}}{\max }\mathrm{corr}\left({\mathrm{\φ}}_1\left(\mathrm{NPQ}\right)\right),{\mathrm{\φ}}_2(\mathrm{MPQ}\left)\right),{\mathrm{\φ}}_3(\mathrm{SF}-{36}_1),\·\·\·,{\mathrm{\φ}}_{10}(\mathrm{SF}-{36}_8))$

（1）

In (1) formula, corr represents the computing function of correlativity;

4) to the finding the solution of (1) formula, think that Φ has following linear forms: Φ (x)=w ^TX, owing to used the nuclear mapping, so its result can not be subjected to the restriction of the linear combination of basis function, used the thought that is similar to KCCA that the optimization problem shown in (1) formula is found the solution, release the maximized solution of consistance between two groups of questionnaires earlier, and then be generalized to the situation of many group questionnaires; Be example with NPQ and two groups of questionnaires of MPQ, establish it and have scale l, i.e. NPQ={NPQ ₁, NPQ ₂..., NPQ _lAnd MPQ={MPQ ₁, MPQ ₂..., MPQ _l, establish u=M _N* NPQ, υ=M _M* MPQ; Make the correlativity maximum of u and υ, be equivalent to and find the solution following optimization problem:

$\underset{M_N,M_M}{\max }\frac{E\left[\mathrm{u\υ}\right]}{\sqrt{E\left[u^2\right]E\left[{\mathrm{\υ}}^2\right]}}---\left(1\right)$

E[wherein] be mathematical expectation, note C _{NPQ, MPQ}Be covariance matrix, then (2) can be expressed as:

$\underset{M_N,M_M}{\max }\frac{M_N^T{C}_{N,M}{M}_M}{\sqrt{M_N^T{C}_{N,N}{M}_N{M}_M^T{C}_{M,M}{M}_M}}---\left(2\right)$

According to the KCCA theory, in optimization aim (3), consider u ^TU and υ ^Tυ rather than original u and υ help to introduce kernel function in optimization aim; Quote two standardization items:

With

It only calculates for simplifying, and can't influence the optimization aim of (3); Simultaneously, as long as levying the dimension in space, the data point number bit of training wants big, the optimum solution of (3)

With

One fixes on set span{ φ (x ₁), φ (x ₂) ..., φ (x _n) and In, wherein x and y are respectively the training sample points of NPQ and MPQ, namely $M_M^{*}={\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_i\mathrm{\φ}\left(x_i\right),$

Use the mode of maximum likelihood to control the model complexity, increase by two regularization term about α and β, obtain following optimization aim expression formula:

$\underset{\mathrm{\α},\mathrm{\β}}{\max }{\mathrm{\α}}^T{K}_X{K}_Y\mathrm{\β}-{\mathrm{\η}}_{\mathrm{\α}}{\left|\right|\mathrm{\α}\left|\right|}^2-{\mathrm{\η}}_{\mathrm{\β}}{\left|\right|\mathrm{\β}\left|\right|}^2---\left(4\right)$

K wherein _X=Σ _iφ (x _i) ^Tφ (x _i),

(4) formula is and finds the solution target.

2. the machine learning method of subjective the differing property of questionnaire of the minimizing traditional Chinese medical science according to claim 1 is characterized in that the represented optimization aim of above-mentioned formula (4) adopts the enclosed solving method to find the solution:

Note w=(α ^T, β ^T) ^T, then being had by representation theorem, the optimum solution of (4) is equivalent to secular equation B ^-1The solution of Aw=pw, p can regard square formation B as ^-1The proper vector of A, wherein:

$A=\left(\begin{array}{cc}0& K_X{K}_Y\\ K_Y{K}_X& 0\end{array}\right)$ $B=\left(\begin{array}{cc}{K}_X{K}_Y& 0\\ 0& K_Y{K}_X\end{array}\right)---\left(5\right)$

Step to above-mentioned solving-optimizing target is carried out following conclusion:

The 1st step: input questionnaire group Q _iAnd Q _j

The 2nd step: calculate questionnaire group Q _iAnd Q _jThe Gram matrix based on radial basis function nuclear

With

The 3rd step: use formula (5) to calculate questionnaire group Q _iAnd Q _jCorrespondence

With

The 4th step: compute matrix

With

Proper vector

With

The 5th step: output is as transformation matrix;

Top step is the enclosed solving method, can directly from training data, obtain transformation matrix, but because it will carry out the feature decomposition of matrix, therefore be only applicable to the little situation of amount of training data, be not more than 1000 examples, use a kind of based on the method for decomposing the index iteration convergence, respectively questionnaire group consistance is separately found the solution, connecting mapping then merges, algorithm uses a w at random as initial value, correlativity is once calculated in every optimization one time, and twice correlativity change is less than 0.5% the time when front and back, and algorithm finishes.

3. the machine learning method of subjective the differing property of questionnaire of the minimizing traditional Chinese medical science according to claim 2 is characterized in that the represented optimization aim of above-mentioned formula (4) adopts following steps to find the solution:

The 1st step: input questionnaire group Q _iAnd Q _j, initializes weights vector w;

The 2nd step: calculate questionnaire group Q _iAnd Q _jThe Gram matrix based on radial basis function nuclear With

The 3rd step: the Gram matrix K based on radial basis function nuclear of calculating weight vectors w _w

The 4th step: use formula (5), calculate questionnaire group Q _iAnd Q _j With

The 5th step: compute matrix

With

Proper vector

With

The 6th step: upgrade $w=M_{Q_i}{M}_{Q_j};$

The 7th step: calculate δ=corr (Q _i* w, Q _j* w);

The 8th step: if δ＞0.5% then jumped to for the 3rd step, otherwise finishes;

Said process is the complexity that exchanges algorithm with the time for, has avoided big square formation is directly carried out feature decomposition, comes down to each composition is carried out based on the finding the solution of method one, and then carries out addition;

Because what said process carried out is to connect after optimizing again, therefore need one to connect the step result is connected, adopt the method shown in the following formula (6) to connect, its objective is the expression formula that obtains an expansion mapping, can be used for the data in future;

$\mathrm{\φ}\left(x\right)=({\mathrm{\Σ}}_i{Q}_i/|\left|{M{Q}_Q}_i\right||+{\mathrm{\Σ}}_i{Q}_j/|\left|M_{Q_j}\right|\left|\right)x---\left(6\right)$

By formula (6), obtain a conversion that can be used for any unknown data

It can change the distribution of unknown data, makes it and existing questionnaire group Q _iAnd Q _jScore value correlativity maximum.